Parallax Distance Calculator
The distance to a star from its parallax angle — in parsecs, light-years, astronomical units and kilometres — with the uncertainty that follows from the measurement error and the distance modulus.
As the Earth orbits the Sun a nearby star shifts against the background by a tiny angle.
How the parallax distance calculator works
As the Earth orbits the Sun a nearby star shifts against the background by a tiny angle. Half that shift is the parallax, and distance in parsecs is simply one over the parallax in arcseconds — the parsec was defined to make it so. Proxima Centauri's 0.768 arcseconds is 1.30 parsecs, 4.25 light-years.
The method fails gently: at a tenth of a milliarcsecond error, a star at 1,000 parsecs has a 10% uncertainty, and the error is asymmetric because a smaller parallax means a larger distance.
Formula: d (pc) = 1 / p (arcsec) = 1000 / p (mas)
Worked examples
| Inputs | Distance (parsecs) | Note |
|---|---|---|
| Proxima Centauri | 1.302 | 1.30 pc, 4.25 ly |
| A star at one milliarcsecond | 1,000 | 1,000 pc, 10% error |
| Betelgeuse, roughly | 168.0672 | a poorly known distance |
FAQFrequently asked questions
What is parallax?
The apparent shift of a nearby star against distant ones as the Earth moves around the Sun. Half the total shift over a year is the parallax angle, and it is tiny — under one arcsecond for every star.
What is a parsec?
The distance at which one astronomical unit subtends one arcsecond — 3.26 light-years. It was defined so that distance is simply one over the parallax.
How far can parallax reach?
Gaia measures to about 0.02 milliarcseconds, giving 10% distances out to a few thousand parsecs. Beyond that, standard candles take over.
Why is the error asymmetric?
Because distance is the reciprocal of parallax. Subtracting the error from a small parallax moves the distance further than adding it does, and at large errors the far limit runs to infinity.
What is the distance modulus?
Five log distance minus five — the difference between a star's apparent and absolute magnitude. With a parallax distance and an apparent magnitude, you have the star's true luminosity.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- CSIRO Space and Astronomy — Australia's national science agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).